1. Definitions

Definition of multi-phase flow
Multi-phase-flow phenomena are, for PHOENICS, those in which,
within the smallest element of space which is considered (i.e.the
computational cell) several distinguishable materials are present.

Examples are:-

suspensions of oil droplets in water, or of water droplets in oil;

the air-snow mixture in an avalanche;

the sand-air mixture in a sandstorm;

the "mushy zone" of mixed solid and liquid metal in a casting
mould;

the water-air mixture in a shower bath;

the gas-oil-water mixture, in the pores within rock, in a
petroleum-recovery process;

droplets of fuel oil, mixed with hot gases, in a combustion
chamber.

Definition of a phase
The above examples employ the word "phase" in the sense customary in
thermodynamics, where the liquid, solid and gas phases are
distinguished.

However, a broader definition of phase is used in PHOENICS. This
allows sand particles of different densities, or steam bubbles of
different sizes, or gas eddies of different temperatures, also to be
regarded as different phases.

The distinction between intermingled and separated multi-phase flows

Often, the multiple phases in the complete domain become sharply
separated. This happens, for example, when the gas flame beneath a
domestic kettle is switched off; for the bubbles rise, the
suspended droplets fall, and a plane unbroken surface forms between
the steam and the water.

The flow is then often called a fully-separated or free-surface
flow.

Both intermingled and separated flows are considered in this
encyclopaedia article.

Simulation methods in PHOENICS

Multi-phase-flow phenomena can be simulated by PHOENICS in four
distinct ways. These are:

as two inter-penetrating continua, each having at each point in
the space-time domain under consideration, its own:

velocity components,

temperature,

composition,

density,

viscosity,

volume fraction,

etc;

as multiple inter-penetrating continua having the same variety
of properties;

as two non-interpenetrating continua, separated by a free
surface; or

as a particulate phase for which the particle trajectories are
computed as they move through a continuous fluid.

Method (1) IPSA for two iterpenetrating continua.

When many phases are present, it is impractical to solve full sets
of Navier-Stokes equations for all of them.

In this method, therefore, only one set of differential equations
is solved, to give the mixture-mean velocities at each point and
time.

Then separate sets of equations are solved, one for each phase,
which govern its relative velocities, i.e.their differences from the
mean.

The latter equations are algebraic ones, which are derived from the
Navier-Stokes equations by neglect of second-order terms.

This entails that the relative velocities are computed by reference
only to the local pressure gradients, the body forces and the inter-
phase friction.

The volume fractions occupied by each phase, at each point and
time, are calculated at the same time.

This method is referred to in the PHOENICS documentation as the
"algebraic-slip" method, with the abbreviation ASLP. Elsewhere in
the scientific literature, it is sometimes called the "drift-flux"
method.

It is embodied in the Advanced Multi-Phase Flow option of PHOENICS;
and it makes use of the open-source Fortran file
GXASLP.HTM .

The axis is along the lower edge of the picture border
The flow is from right to left.
The cylindrical vessel is rotating at high speed, so that the
liquids are flung to the outside, i.e.upward on the diagram.